sëgi¸odôcv®ot¹othanhho¸
®Òthichän®éituyÓnhäcsinhgiáilíp12
Tr−êngthpthmrång


Thêigianlmbi:120phót
Ngythi:03/12/2009



:1.ThÝsinhchØ®−îcsödôngm¸ytÝnhCasiofx$570MStrëxuèng.
2.NÕukh«ngnãig×thªm,h4ytÝnhchÝnhx¸c®Õn6ch÷sèthËpph©n.
3.NÕutÝnhgãcth×tÝnhchÝnhx¸c®Õn®é,phót,gi©y.
 
(2®iÓm)Chohmsè
+
=
(C).
T×mto¹®étiÕp®iÓmcñatiÕptuyÕnvíi(C)®iqua®iÓmA(1;*2).
(2®iÓm)Chohmsè
−
−
=
(C).T×mto¹®éhai®iÓmA,B
thuéchainh¸nhkh¸cnhaucña(C)saocho®édi®o¹nABng¾nnhÊt.
(2®iÓm)ChoP(x)=x
4
+ax
3
+bx
2
+cx+d.BiÕtP(1)=*1807,
P(2)=*14893,P(2008)=*8086401493,P(2010)=8130602003.
H=ytÝnh:P(2009)?
(2®iÓm)T×mnghiÖm
(
)
π
∈
cñaph−¬ngtr×nh:

( )




=+−−
 (2®iÓm)Choa>0,b>0va+b=1.T×mgi¸trÞlínnhÊt,nhá
nhÊtcñabiÓuthøcF=a
12
+b
12
.
!(2®iÓm)Cho

−+=
.
TÝnhtængtÊtc¶c¸chÖsècñac¸csèh¹ngtrongkhaitriÓncñaP(x).
"(2®iÓm)Cã15häcsinhgiáilípA,12häcsinhgiáilípB,9häc
sinhgiáilípC.TÝnhx¸csuÊt®Óchän®−îc10emdùthiHSGtØnhcã®ñhäc
sinh3líptrªnbiÕtkh¶n¨ngcñac¸cemlnh−nhau.
#(2®iÓm)ChoABC.Trªnc¹nhAClÊy®iÓmDsaochoAD=3DC.
biÕtgãcAb»ng40
0
vgãc
BDC=65
0
.TÝnhsè®ocñagãcBCA.
$(2®iÓm)ChotødiÖnABCDbiÕt:AB=10,BC=11,CA=12,DA
=DB=DC=9.TÝnhthÓtÝchtødiÖnABCD.
%(2®iÓm)Chohmsè
+
+
=
.
TÝnhtæng:

+++++=
sëgi¸odôcv®ot¹othanhho¸
§¸p¸n®Òthichän®éituyÓnhäcsinhgiái12
Tr−êngthpthmrång


Thêigianlmbi:120phót
Ngythi:03/12/2009



:1.ThÝsinhchØ®−îcsödôngm¸ytÝnhCasiofx$570MStrëxuèng.
2.NÕukh«ngnãig×thªm,h4ytÝnhchÝnhx¸c®Õn6ch÷sèthËpph©n.
3.NÕutÝnhgãcth×tÝnhchÝnhx¸c®Õn®é,phót,gi©y.
 
(2®iÓm)Chohmsè
+
=
(C).
T×mto¹®étiÕp®iÓmcñatiÕptuyÕnvíi(C)®iqua®iÓmA(1;*2).
x
1
≈
*2,618034
y
1
≈
*4,236068
x
2
≈
*0,381966
y
2
≈
0,236068
(2®iÓm)Chohmsè
−
−
=
(C).T×mto¹®éhai®iÓmA,B
thuéchainh¸nhkh¸cnhaucña(C)saocho®édi®o¹nABng¾nnhÊt.
x
A
≈
1,563771
y
A
≈
0,850443
x
B
≈
0,436229
y
B
≈
1,977984
(2®iÓm)ChoP(x)=x
4
+ax
3
+bx
2
+cx+d.BiÕtP(1)=*1807,
P(2)=*14893,P(2008)=*8086401493,P(2010)=8130602003.
H=ytÝnh:P(2009)?
=9992009
(2®iÓm)T×mnghiÖm
(
)
π
∈
cñaph−¬ngtr×nh:

( )




=+−−
x
1
≈
0,392699
x
2
≈
1,178097
x
3
≈
1,963495
x
4
≈
2,748894
 (2®iÓm)Choa>0,b>0va+b=1.T×mgi¸trÞlínnhÊt,nhá
nhÊtcñabiÓuthøcF=a
12
+b
12
.
MaxF=1
minF
≈
0,000488
!(2®iÓm)Cho

−+=
.
TÝnhtængtÊtc¶c¸chÖsècñac¸csèh¹ngtrongkhaitriÓncñaP(x).
≈
3,387260
"(2®iÓm)Cã15häcsinhgiáilípA,12häcsinhgiáilípB,9häc
sinhgiáilípC.TÝnhx¸csuÊt®Óchän®−îc10emdùthiHSGtØnhcã®ñhäc
sinh3líptrªnbiÕtkh¶n¨ngcñac¸cemlnh−nhau.
≈
0,957719
#(2®iÓm)ChoABC.Trªnc¹nhAClÊy®iÓmDsaochoAD=3DC.
biÕtgãcAb»ng40
0
vgãc
BDC=65
0
.TÝnhsè®ocñagãcBCA.
≈
102
0
39’9,7”
$(2®iÓm)ChotødiÖnABCDbiÕt:AB=10,BC=11,CA=12,DA
=DB=DC=9.TÝnhthÓtÝchtødiÖnABCD.
≈
108,581479
%(2®iÓm)Chohmsè
+
+
=
.
TÝnhtæng:

+++++=
≈
24,566849